A027055 a(n) = T(n, n+4), T given by A027052.

1, 18, 59, 146, 319, 652, 1281, 2456, 4637, 8670, 16111, 29822, 55067, 101528, 187013, 344276, 633561, 1165674, 2144419, 3944650, 7255831, 13346084, 24547849, 45151152, 83046581, 152747190, 280946647, 516742262, 950438067

Offset

4,2

Links

G. C. Greubel, Table of n, a(n) for n = 4..1003

Index entries for linear recurrences with constant coefficients, signature (4,-5,2,-1,2,-1).

Formula

From Colin Barker, Feb 19 2016: (Start)

a(n) = 4*a(n-1) -5*a(n-2) +2*a(n-3) -a(n-4) +2*a(n-5) -a(n-6) for n>9.

G.f.: x^4*(1+14*x-8*x^2-2*x^3-5*x^4+4*x^5)/((1-x)^3*(1-x-x^2-x^3)).

(End)

a(n) = A001590(n+5) -n*(5+n), n>=4. - R. J. Mathar, Jun 15 2020

Maple

seq(coeff(series(x^4*(1+14*x-8*x^2-2*x^3-5*x^4+4*x^5)/((1-x)^3*(1-x-x^2-x^3)), x, n+1), x, n), n = 4..40); # G. C. Greubel, Nov 06 2019

Mathematica

LinearRecurrence[{4, -5, 2, -1, 2, -1}, {1, 18, 59, 146, 319, 652}, 40] (* G. C. Greubel, Nov 06 2019 *)

Prog

(PARI) my(x='x+O('x^40)); Vec(x^4*(1+14*x-8*x^2-2*x^3-5*x^4+4*x^5)/((1-x)^3*(1-x-x^2-x^3))) \\ G. C. Greubel, Nov 06 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( x^4*(1+14*x-8*x^2-2*x^3-5*x^4+4*x^5)/((1-x)^3*(1-x-x^2-x^3)) )); // G. C. Greubel, Nov 06 2019
(Sage)
def A027053_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P(x^4*(1+14*x-8*x^2-2*x^3-5*x^4+4*x^5)/((1-x)^3*(1-x-x^2-x^3))).list()
a=A027053_list(40); a[4:] # G. C. Greubel, Nov 06 2019
(GAP) a:=[1, 18, 59, 146, 319, 652];; for n in [7..40] do a[n]:=4*a[n-1] -5*a[n-2]+2*a[n-3]-a[n-4]+2*a[n-5]-a[n-6]; od; a; # G. C. Greubel, Nov 06 2019

Crossrefs

Sequence in context: A155155 A048356 A244806 * A056448 A056438 A218617

Adjacent sequences: A027052 A027053 A027054 * A027056 A027057 A027058

Keyword

nonn,easy

Author

Clark Kimberling

Status

approved